Search results

An '''entitative [[graph (mathematics)|graph]]''' is an element of the [[graph theory|graphical]] [[syntax]] for [[logic]] that [[Charles ...Qualitative Logic", MS 736 (c. 1886), pp. 101–115 in ''The New Elements of Mathematics by Charles S. Peirce, Volume 4, Mathematical Philosophy'', [[Carolyn Eisele

...rgone rapid expansion, with topics ranging from automobiles, to people, to mathematics. <!-- This line break means that the next element should appear below all other elements, regardless of alignment. -->

...In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math> * [[Relation (mathematics)|Relation]]

A '''boolean domain''' <math>\mathbb{B}</math> is a generic 2-element [[set]], say, <math>\mathbb{B} = \{ 0, 1 \},</math> whose elements are inte * [[Relation (mathematics)|Relation]]

...> is an arbitrary set and where <math>\mathbb{B}\!</math> is a generic two-element set, typically <math>\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{t * [[Relation (mathematics)|Relation]]

...es up a pair of simple but instructive examples from each of the realms of mathematics and semiotics. ==Examples from mathematics==

: ''For an introduction to graph theory see [[Graph (mathematics)]]''. ...'''graph theory''' has for its subject matter the properties of ''[[graph (mathematics)|graphs]]''. Informally speaking, a graph is a set of objects called ''poi

Here, we describe the [[mathematics|mathematical]] meaning of '''transfinite ordinal numbers'''. They were int ...keep this section intuitive and understandable with almost no knowledge of mathematics. -->

'''Hypostatic abstraction''' is a formal operation that takes an element of information, as expressed in a proposition <math>X ~\text{is}~ Y,\!</mat ...ntroduced [[Charles Sanders Peirce]] (CP&nbsp;4.235, &ldquo;[[The Simplest Mathematics]]&rdquo; (1902), in ''Collected Papers'', CP&nbsp;4.227&ndash;323).

...laws in general it therefore suffices to understand them for just this two-element Boolean algebra. ...n''-ary operations ''f'':&nbsp;''X''^''n''&rarr;''X'' on a ''k''-element set ''X'', there are therefore 2²^{^''n''} ''n

...al reducibility''' have to do with the extent to which a given [[relation (mathematics)|relation]] is determined by a set of other relations, called the ''relatio ...for <math>(s, i),\!</math> tells us that <math>L\!</math> has just the one element <math>(o, s, i)\!</math> over each point of <math>S \times I.\!</math> All

In mathematics, a '''finitary relation''' is defined by one of the formal definitions give ...gned to deal with empirical data, and experience is always finite, whereas mathematics is nothing if not concerned with infinity, at the very least, potential inf

...oint of <math>\mathbb{B}^k~\!</math> is the unique point in the ''[[fiber (mathematics)|fiber]] of truth'' <math>[|s|]~\!</math> of a ''singular proposition'' <ma : A ''[[boolean domain]]'' <math>\mathbb{B}~\!</math> is a generic 2-element set, for example, <math>\mathbb{B} = \{ 0, 1 \},~\!</math> whose elements a

...et satisfying certain equations. Just as group theory deals with [[Group (mathematics)|groups]], and linear algebra with [[vector spaces]], so does Boolean algeb ...to mathematical logic, digital logic, and the set-theoretic foundations of mathematics, among other applications. Boolean algebra has a rich mathematical theory,

...laws in general it therefore suffices to understand them for just this two-element Boolean algebra. ...n''-ary operations ''f'':&nbsp;''X''^''n''&rarr;''X'' on a ''k''-element set ''X'', there are therefore 2²^{^''n''} ''n

...n (mathematics)|relational]] form which translates into being the [[graph (mathematics)|map]] of a ''realization'' [[digital network|network]] (see [[VHDL]]). ...nclude simple operations such as incrementing the value of a variable data element. More complex computations may involve many operations and data elements t

...e result, illustrated by means of a digraph picture, where the "no change" element (''dx'')(''dy'') is drawn as a loop at the point ''x y''. ...he relationship between the pragmatic maxim and what are commonly known in mathematics as ''representation principles''. As it turns out, with regard to its form

# Base. Any element of the alpha set <math>\Alpha\!</math> is a formula of <math>\mathcal{L}</m * [[Relation (mathematics)|Relation]]

'''Relation composition''', or the composition of [[relation (mathematics)|relations]], is the generalization of function composition, or the composi The first order of business is to define the operation on [[relation (mathematics)|relations]] that is variously known as the ''composition of relations'', '

| '''IF''' we know that the element <math>x\!</math> is of the type <math>X\!</math> | '''THEN''' we know that the element <math>f(x)\!</math> is of the type <math>Y.\!</math>

...particular conception of truth, such as those used in art, ethics, logic, mathematics, philosophy, the sciences, or any discussion that either mentions or makes ...t into question and needs to be evaluated. Depending on the context, this element might be called an ''artefact'', ''expression'', ''image'', ''impression'',

...tion of [[truth]], such as those used in [[art]], [[ethics]], [[logic]], [[mathematics]], [[philosophy]], the [[science]]s, or any discussion that either mentions ...t into question and needs to be evaluated. Depending on the context, this element might be called an ''artefact'', ''expression'', ''image'', ''impression'',

...tion of [[truth]], such as those used in [[art]], [[ethics]], [[logic]], [[mathematics]], [[philosophy]], the [[science]]s, or any discussion that either mentions ...t into question and needs to be evaluated. Depending on the context, this element might be called an ''artefact'', ''expression'', ''image'', ''impression'',

...ut into question and needs to be evaluated. Depending on the context, this element might be called an ''artefact'', ''expression'', ''image'', ''impression'', ...er'', or a ''language'' to which the representation bears some [[relation (mathematics)|relation]].

...ningful entities may include almost any kind of informative or significant element — the generic terms ''sign'' or ''representation'' will continue to serve ...ningful entities may include almost any kind of informative or significant element, described by the generic terms ''[[sign (semiotics)|sign]]'' or ''[[repre

...ningful entities may include almost any kind of informative or significant element — the generic terms ''sign'' or ''representation'' will continue to serve ...ningful entities may include almost any kind of informative or significant element, described by the generic terms ''[[sign (semiotics)|sign]]'' or ''[[repre

...>S\!</math> be the set of rooted trees and let <math>S_0\!</math> be the 2-element subset of <math>S\!</math> that consists of a rooted node and a rooted edge ...ve just provided. Although equational forms of reasoning are paramount in mathematics, they are less familiar to the student of conventional logic textbooks, who

...>S\!</math> be the set of rooted trees and let <math>S_0\!</math> be the 2-element subset of <math>S\!</math> that consists of a rooted node and a rooted edge ...ve just provided. Although equational forms of reasoning are paramount in mathematics, they are less familiar to the student of conventional logic textbooks, who

...e result, illustrated by means of a digraph picture, where the "no change" element <math>(\operatorname{d}p)(\operatorname{d}q)</math> is drawn as a loop at t ...he relationship between the pragmatic maxim and what are commonly known in mathematics as ''representation principles''. As it turns out, with regard to its form

...or <math>\lambda\!</math> in formal languages, where it forms the identity element for concatenation. To make it visible in context, it may be denoted by the ...lustrated by means of a digraph picture, where the &ldquo;no change&rdquo; element <math>(\mathrm{d}p)(\mathrm{d}q)\!</math> is drawn as a loop at the point <

...m <math>(o, s, i)\!</math> called an ''elementary relation'', that is, one element of the relation's set-theoretic extension. ...\!</math> is an equivalence relation on a set <math>X,\!</math> then every element <math>x\!</math> of <math>X\!</math> belongs to a unique equivalence class

...t into question and needs to be evaluated. Depending on the context, this element might be called an ''artefact'', ''expression'', ''image'', ''impression'', ...er'', or a ''language'' to which the representation bears some [[relation (mathematics)|relation]].

...e result, illustrated by means of a digraph picture, where the "no change" element <math>(\mathrm{d}x)(\mathrm{d}y)\!</math> is drawn as a loop at the point < ...he relationship between the pragmatic maxim and what are commonly known in mathematics as ''representation principles''. As it turns out, with regard to its form

where the "no change" element (dx)(dy) is drawn as a loop at the point x·y. known in mathematics as "representation principles". As it turns out,

...t'' needs to be understood in a way that is analogous to its definition in mathematics, where it means ''[[orthogonal]]'', or its definition in statistics, where ...logism in logic, by establishing the same “fictional” status for logic and mathematics that he claims for universals. Now by proving logic ''fictional'', Peirce b

...mployed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or ''[[semeiotic]]'', that he is larg ...s huge output is still unpublished. An innovator in fields such as logic, mathematics, [[philosophy of science]], research methodology, [[semiotics]], [[epistemo

...ngly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some. Hence the extension and comprehens ...designation of an even far more important procedure, whereby a transitive element of thought is made substantive, as in the grammatical change of an adjectiv

...l <math>\mathrm{X}\!</math> of the genus <math>\mathrm{x}\!</math> and the element <math>x\!</math> of the set <math>X\!</math> as we pass between the two sty ...d here by square brackets. I have already quoted from the &ldquo;Logic of Mathematics&rdquo; paper in a related connection. Here are the links to those excerpts

...and formulas without causing a confusion between the term "Color" and the element ''C'', let me change the term "Color" to "Hue". * [[Graph (mathematics)|Graph]]

...oldsymbol\lambda\!</math> in formal languages, where it forms the identity element for concatenation. It may be given visible expression in this context by m [[Category:Mathematics]]

...the derivatives and the differentials of any functions usually come up in mathematics, namely, in relation to the problem of computing "locally linear approximat ...lexibility of this order is very useful, and it is quite common throughout mathematics. In this discussion, I will invoke its application under the name of the '

| element x in X an element f x in Y; whenever possible we write f x | occur throughout mathematics.

...n, [http://www.math.uic.edu/~kauffman/Arithmetic.htm Box Algebra, Boundary Mathematics, Logic, and Laws of Form]. ...le, simulation, and so on forms an extremely important complex of ideas in mathematics, there being recognized under the generic idea of ''structure-preserving ma

...or <math>\lambda\!</math> in formal languages, where it forms the identity element for concatenation. To make it visible in context, it may be denoted by the ...consider it a good thing to always know what we are talking about. Where mathematics encourages tolerance for uninterpreted symbols as intermediate terms, logic

...> is a string over <math>\mathfrak{A}</math> and if <math>s\!</math> is an element of <math>\mathfrak{L},</math> then it is customary to call <math>s\!</math> ...</math> is a sentence of <math>\mathfrak{L},</math> <math>t\!</math> is an element of <math>\mathfrak{A},</math> and

It has been appreciated in mathematics and physics for at least a century that course have many other uses in theoretical and applied mathematics.

...tion to the context and the purpose of the judgment are said to involve an element of 'art', in a sense that is judged to distinguish them from 'science', and * [[Relation (mathematics)|Relation]]

...by &epsilon; or &lambda; in formal languages, where it forms the identity element for concatenation. To make it visible in this text, I denote it by the equ ...consider it a good thing to always know what we are talking about. Where mathematics encourages tolerance for uninterpreted symbols as intermediate terms, logic

...ngly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some. Hence the extension and comprehens ...ngly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some. Hence the extension and comprehens

...e of the political parties adopted his Save the Mall position as the major element of its platform. A ban on future streeting of pedestrian areas has now be ...orm advocate, actor, and professor [[Les Golden]], attorney Robert Ransom, mathematics professor Richard Compton, Len Mueller, jeweler Bob Ryan, urban studies pro

...{}^{\prime\prime}</math> in formal languages, where it forms the identity element for concatenation. To make it visible in this text, it may be denoted by t ...consider it a good thing to always know what we are talking about. Where mathematics encourages tolerance for uninterpreted symbols as intermediate terms, logic

...}^{\prime\prime}\!</math> in formal languages, where it forms the identity element for concatenation. To make it visible in this text, it may be denoted by t ...consider it a good thing to always know what we are talking about. Where mathematics encourages tolerance for uninterpreted symbols as intermediate terms, logic

It has been appreciated in mathematics and physics for at least a century that an isomorphism is almost totally us ...computing would of course have many other uses in theoretical and applied mathematics.

...blems of logic, that of producing a method for the discovery of methods in mathematics.</p> <i>American Journal of Mathematics</i>, 7(2), 180&ndash;202, (1885).</p>

| NEM 4 = 'The New Elements of Mathematics', Vol. 4, third element, the one we are in fact making explicit only

|'American Journal of Mathematics', vol. 7, no. 2, pp. 180-202, 1885. | Still, a satisfactory evolutionary logic of mathematics remains a

where the "no change" element (dx)(dy) is drawn as a loop at the point x y. known in mathematics as "representation principles". As it turns out,

...tterns won't have had any exposure to computer science theory and discrete mathematics so they put it in their as a means of "blinding their readers with (pseudo- ...thematics, "discrete analysis of individual systems" and that this type of mathematics excludes the use of probability. I think that this may be the argument that

be cast or recast as a three-place relation, one whose staple element of element of the relation's set-theoretic extension.

...tion to the context and the purpose of the judgment are said to involve an element of "art", in a sense that is judged to distinguish them from "science", and * [[Relation (mathematics)|Relation]]

...tified by deduction or by induction, at least, not wholly, but involves an element of hypothesis. In ancient times, this mode of inference to an explanatory If this were an abstract discussion in mathematics or philosophy, these differences would constitute little more than variant